Since the measurement of rotation and dispersion profiles in
ellipticals has only recently become practical, the most extensive
stellar-kinematic measurements available are those of central velocity
dispersions . These
allow us to estimate central mass-to-light ratios
(section 4.2.3). Also, the discovery of
a correlation between
and metallicity
indicates that ellipticals are at least a two-parameter family
(section 4.2.4). A necessary tool for
both of these applications is a fundamental correlation between
and the total blue
luminosity LB
(Faber and Jackson
1976),
which has the approximate form
LBn, n 4.

This relation has since been confirmed by many authors (S2BS;
Schechter and Gunn
1978;
Schechter 1980;
Terlevich et al. 1981;
Tonry and Davis 1981b;
de Vaucouleurs and
Olson 1982,
and others), who added
more measurements and refined the parameters n and the zero point.
Since LB is proportional to the adopted distance and
is not, the
Faber-Jackson relation also provides a new way of measuring relative
distances. In particular, it has been used to map the velocity field
in the local supercluster, and thereby to derive the Local Group infall
velocity W0 toward Virgo. Two independent solutions
give the following results:

Figure 33. Correlations between central
velocity dispersions and
absolute magnitudes MB for elliptical galaxies and
for bulges of unbarred and barred disk galaxies
(Kormendy and
Illingworth 1982b).
Edge-on galaxies are omitted. The solid line is in each case the
Ln relation
for SA0-bc galaxies, n = 7.8(+1.9, -1.3),
21 = 208 km
s-1. The two very discrepant galaxies, NGC 1172 (upper)
and NGC 7457,
have been omitted from this solution. The dashed line is a
least-squares fit for the ellipticals, n = 5.4(+0.9, -0.7),
21 = 217 km
s-1.
Zero points for least-squares fits to various subsamples of the
data are given under the figure. For each set of solutions the
value of n is fixed.

Recent work suggests that the Faber-Jackson relation may not be a
simple power law. At the low-luminosity end, a downward curvature of
the relation in Figure 33 is indicated by
Tonry's (1981)
analysis of galaxies down to MB = -18.0. This study
has the advantage that the
galaxies are all in the Virgo cluster, so relative distance errors
cannot affect the value of n. For ellipticals fainter than
MB ~ - 20, Tonry finds that
LB3.2±0.2.
Similarly,
Davies et al. (1983)
find n = 2.4 ± 0.9 for 14 ellipticals fainter than
MB = -20, and
n = 4.2 ± 0.9 for 30 brighter ellipticals. If this effect is
confirmed
in larger samples, several explanations are possible. (1) The mass-to-light
ratio may be a steeper function of luminosity in faint galaxies
than in bright ones; see section 4.2.3.
(2) Rotation may provide some of the
dynamical support in low-luminosity ellipticals, which are known to
rotate rapidly (section 4.2.6). (3)
Velocity dispersion gradients may be
averaged by the large measuring aperture used,
3" × 12". This is a
special problem for faint ellipticals because they, have small dynamical
characteristic radii. If the
- rc
relation of Figure 22 holds for these galaxies, they have core radii
rc ~ 0.5". Any dispersion
gradients generally begin just outside r = rc (see
Fig. 35). But
rc is much smaller than the measuring aperture.

At the high-luminosity end, Malumuth and Kirshner
(1981,
Fig. 1) suggest that the
log -
MB correlation levels off, in that brightest
cluster galaxies do not have larger dispersions than slightly fainter
galaxies. The deviation from the adopted
Ln
relation is especially
large for three cD galaxies measured. However, most of this effect is
due to the contribution to MB of the cD halo; when
this is removed
the galaxies do not deviate significantly. As noted by Malumuth and
Kirshner, this is consistent with the assumption (see
section 3.3.4)
that the halos are dynamically distinct features added to basically normal,
although very bright, ellipticals.

Table 4. ZERO POINTS OF Ln
RELATIONS

E (n = 5.4):

21 =

217 ± 6 km s-1

E (n=7.8):

21 =

222 ± 6 km s-1

SA0 :

218 ± 10 km s-1

SA0 :

211 ± 9 km s-1

SAa-bc :

217 ± 9 km s-1

SAa-bc :

205 ± 7 km s-1

SB0-b :

185 ± 10 km s-1

SB0-b :

172 ± 10 km s-1

In section 3.4.1 I discussed a
number of physical differences between
ellipticals and the bulges of spiral galaxies. The Faber-Jackson
relation provides another probe of such differences. Interestingly,
the nuclear dynamics of ellipticals and normal bulges are found to be
indistinguishable.

Early reports seemed to tell a different story.
Whitmore, Kirshner and
Schechter (1979)
and Whitmore and Kirshner
(1981,
hereafter collectively WKS) found that ellipticals and S0s have the same
Ln relation,
but bulges of spiral galaxies have velocity dispersions smaller by
17 ± 8% than ellipticals of the same luminosity. If
we use as the zero point of the
Ln relation the
dispersion 21 at
MB = - 21(H0 = 50 km s-1
Mpc-1), then WKS found
21 = 228
± 11 km s-1 in ellipticals,
220 ± 15 km s-1 in S0 bulges and 190 ± 10
km s-1 in
spiral bulges. All bulge magnitudes were corrected for disk light as
in section 3.4.3. Several effects could
contribute to the above difference.
(1) Much of the photometry used was not accurate enough for reliable
profile decomposition. (2) Rotation of bulges would decrease the
amount of velocity dispersion required to support the galaxy. However,
S0 bulges rotate as rapidly as those of spirals
(section 4.2.6) and are not
colder than ellipticals. (3) The bulges could have lower M/L values
due to recent star formation. In fact,
Whitmore and Kirshner
(1981)
make the prophetic statement that "most of the spiral bulges do fall
very close to the [Ln] line for
ellipticals, and only a few
galaxies (perhaps NGC 4303 and NGC 4321 . . . ) undergoing a recent burst
[of star formation] provide the increased scatter and the gap with the
ellipticals."

Recently,
Kormendy and
Illingworth (1982b)
have re-examined the
Ln relation
for disk-galaxy bulges, motivated by the following
worries about the WKS analysis. First, many WKS "bulges" clearly
contain Population I material. Essentially, the galaxies are too late in
type to contain bulges which resemble ellipticals. What is the
Ln
relation for bulges, like those of M31 and M81, which are similar to
ellipticals? Second, we will see in
section 5 that bulges of barred galaxies
are more disk-like than SA bulges. Do they also have different
Ln
relations? Third, Kormendy and Illingworth retain only those galaxies
with photometrically well determined bulge magnitudes. Finally, they
verify that plausible Virgocentric flow fields do not affect the
conclusions.

The results are shown in Figure 33. Galaxies
which clearly have
young stars in their nuclei are omitted (e.g., NGC 4321, see the
spectrophotometry of
Turnrose 1976).
There is then no difference in the
slope or zero point for ellipticals, or bulges of unbarred S0 or Sa-bc
galaxies. On the other hand, many bulges of barred galaxies, even
SB0s, have lower dispersions than SA bulges of the same luminosity. A
possible interpretation is discussed in
section 5.2.

Evidently the difference in zero point found by WKS was due to the
inclusion of late-type galaxies whose disks contribute light even at
the center, and barred galaxies whose bulges differ systematically from
SA bulges. The global differences between ellipticals and ordinary
bulges are not reflected in their central dynamics, to the accuracy of
the present observations. This is not implausible if the global
differences are caused by a combination of rotation and the disk
potential in bulges; neither effect should be very important near the
center.